依据马蹄变换的混沌流微混合器
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摘要
为了实现微流控芯片对痕量试样的快速、均匀混合,依据"马蹄变换"数学模型,对流体进行"挤压拉伸"、"弯曲折叠"和"逆变换-交集"操作.基于此借助符号动力学系统计算出了"马蹄变换"后的李雅普诺夫指数,从理论上证明了,当满足"挤压"幅度0<λ<1/2且"拉伸"幅度μ>2时,上述操作能够在低雷诺数的层流条件下,成功诱发混沌流.在此基础上,设计并制作了一款由4个"马蹄变换"混合单元组成,有效混合距离为13 mm的微混合器.利用COMSOL软件得到的数值仿真结果表明:当Re≥1时,流体的佩克莱数Pe≥10,此时微混合器诱发的混沌流将随着流速的加快而增强,并逐步成为促进混合的主要因素;当Re=10时,经4个混合单元后,试样的浓度方差σ=0.054,混合效果接近均匀.对微混合器芯片进行的可视化测试结果表明,荧光显微镜拍摄到的示踪剂颜色变化与仿真结果中的表面浓度云图一致;而不同pH试样的混合测试结果则证明了,基于"马蹄变换"数学模型设计的微混合器能够产生混沌流且实际效果理想.
To achieve rapid and uniform mixing of trace samples, based on the mathematical model of "Horseshoe Transformation", a series of operations on fluids, such as "extrusion stretching", "curved folding", and "inverse transformation-intersection" were carried out.Theoretical calculation show that when squeeze amplitude 0<λ<1/2 and stretch amplitude μ>2, the transformation could induce chaos flow successfully under laminar flow with low Reynolds number. Based on theoretical calculations, a mixer which consists of 4 mixing units with the effective mixing length of 13 mm was designed and manufactured. The numerical simulation results by COMSOL show that when Re≥1 and the Peclet Number Pe≥10, the chaotic flow intensity increased with the flow rate and gradually became the main factor to promote mixing. When Re=10, after passing through 4 "Horseshoe Transformation" mixing units, the concentration variance σ=0.054, and the mixing effect was nearly uniform. The visualization test of mixer chip show that the color change of the tracer photographed by the fluorescence microscope was consistent with the surface concentration cloud in the simulation result. Moreover, the mixing test of different pH value samples proved that the micromixer based on the "Horseshoe Transformation" can generate chaos flow and achieve a satisfactory mixing effect.
To achieve rapid and uniform mixing of trace samples, based on the mathematical model of "Horseshoe Transformation", a series of operations on fluids, such as "extrusion stretching", "curved folding", and "inverse transformation-intersection" were carried out.Theoretical calculation show that when squeeze amplitude 0<λ<1/2 and stretch amplitude μ>2, the transformation could induce chaos flow successfully under laminar flow with low Reynolds number. Based on theoretical calculations, a mixer which consists of 4 mixing units with the effective mixing length of 13 mm was designed and manufactured. The numerical simulation results by COMSOL show that when Re≥1 and the Peclet Number Pe≥10, the chaotic flow intensity increased with the flow rate and gradually became the main factor to promote mixing. When Re=10, after passing through 4 "Horseshoe Transformation" mixing units, the concentration variance σ=0.054, and the mixing effect was nearly uniform. The visualization test of mixer chip show that the color change of the tracer photographed by the fluorescence microscope was consistent with the surface concentration cloud in the simulation result. Moreover, the mixing test of different pH value samples proved that the micromixer based on the "Horseshoe Transformation" can generate chaos flow and achieve a satisfactory mixing effect.
引文
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[14]WANG Ruijin, LIJIN Beiqi, SHI Dongdong, et al. Investigation on the splitting-merging passive micromixer based on Baker's transformation[J]. Sensors and Actuators B: Chemical, 2017, 249: 395. DOI:10.1016/j.snb.2017.04.087
[15]SMALE S. Finding a horseshoe on the beaches of Rio[J]. The Mathematical Intelligencer, 1998, 20(1): 39. DOI:10.1007/ BF03024399
[16]ZHANG He, LIU Xiaowei, TIAN Li, et al. Miscible organic solvents soak bonding method use in a PMMA multilayer microfluidic device[J]. Micromachines, 2014, 5(4): 1416. DOI:10.3390/mi5041416
[17]YANG Jun, QI Li, CHEN Yi, et al. Design and fabrication of a three dimensional spiral micromixer[J]. Chinese Journal of Chemistry, 2013, 31(2): 209. DOI:10.1002/cjoc.201200922
[2]MEIJER H E H, SINGH M K, KANG T G, et al. Passive and active mixing in microfluidic devices[J]. Macromolecular Symposia, 2010, 279(1): 201. DOI:10.1002/masy.200950530
[3]赵玉潮, 应盈, 陈光文, 等. T形微混合器内的混合特性[J]. 化工学报, 2006, 57(8): 1884ZHAO Yuchao, YING Ying, CHEN Guangwen, et al. Characterization of micro-mixing in T-shaped micro-mixer[J]. Journal of Chemical Industry and Engineering, 2006, 57(8): 1884. DOI:10.3321/j.issn:0438-1157.2006.08.023
[4]CHEN Zhuo, ZHANG Ruiqi, WANG Xiaona. CFD study of flow-diffusion process in Y-shape micromixer[J]. Journal of Central South University, 2016, 23(4): 969. DOI:10.1007/s11771-016-3144-7
[5]LI Tiechuan, CHEN Xueye. Numerical investigation of 3D novel chaotic micromixers with obstacles[J]. International Journal of Heat and Mass Transfer, 2017, 115: 278. DOI: 10.1016/j.ijheatmasstransfer.2017.07.067
[6]HUSAIN A, KHAN F A, HUDA N, et al. Mixing performance of split-and-recombine micromixer with offset inlets[J]. Microsystem Technologies, 2018, 24(3): 1511. DOI:10.1007/s00542-017-3516-4
[7]XIE Tingliang, XU Cong. Numerical and experimental investigations of chaotic mixing behavior in an oscillating feedback micromixer[J]. Chemical Engineering Science, 2017, 171: 303. DOI:10.1016/j.ces.2017.05.040
[8]STROOCK A D, DERTINGER S K W, AJDARI A, et al. Chaotic mixer for microchannels[J]. Science, 2002, 295(5555): 647. DOI:10.1126/science.1066238
[9]SONG Hongjun, YIN Xiezhen, BENNETT D J. Optimization analysis of the staggered herringbone micromixer based on the slip-driven method[J]. Chemical Engineering Research and Design, 2008, 86(8): 883. DOI:10.1016/j.cherd.2008.03.015
[10]WIGGINS S, OTTINO J M. Foundations of chaotic mixing: one contribution of 11 to a Theme‘Transport and mixing at the microscale’[J]. Royal Society of London Transactions Series A, 2004, 362(1818): 937. DOI:10.1098/rsta.2003.1356
[11]CARRIèRE P. On a three-dimensional implementation of the baker's transformation[J]. Physics of Fluids, 2007, 19(11): 937. DOI:10.1063/1.2804959
[12]YASUI T, OMOTO Y, OSATO K, et al. Microfluidic Baker's transformation device for three-dimensional rapid mixing[J]. Lab on A Chip, 2011, 11(19): 3356. DOI:10.1039/c1lc20342h
[13]NEERINCX P E, DENTENEER R P J, PEELEN S, et al. Compact mixing using multiple splitting, stretching, and recombining flows[J]. Macromolecular Materials and Engineering, 2011, 296(3/4): 349. DOI:10.1002/mame.201000338
[14]WANG Ruijin, LIJIN Beiqi, SHI Dongdong, et al. Investigation on the splitting-merging passive micromixer based on Baker's transformation[J]. Sensors and Actuators B: Chemical, 2017, 249: 395. DOI:10.1016/j.snb.2017.04.087
[15]SMALE S. Finding a horseshoe on the beaches of Rio[J]. The Mathematical Intelligencer, 1998, 20(1): 39. DOI:10.1007/ BF03024399
[16]ZHANG He, LIU Xiaowei, TIAN Li, et al. Miscible organic solvents soak bonding method use in a PMMA multilayer microfluidic device[J]. Micromachines, 2014, 5(4): 1416. DOI:10.3390/mi5041416
[17]YANG Jun, QI Li, CHEN Yi, et al. Design and fabrication of a three dimensional spiral micromixer[J]. Chinese Journal of Chemistry, 2013, 31(2): 209. DOI:10.1002/cjoc.201200922